Three years after LeBron James declared he was taking his talents to South Beach, downtown Miami has officially gotten over the slight.

James famously picked South Beach as his post-Cleveland destination when he announced his decision on a live ESPN interview in 2010. And while “taking my talents to South Beach” survives as a catch phrase, the remark didn’t sit well with the tax-funded agency promoting downtown Miami as a place to live and work.

Miami’s Downtown Development Authority in 2010 launched a “Get It Right” campaign to link the Heat to its downtown home, including paying a local PR firm to remind the national media where James plays. “We’re fine with TNT showing visuals of South Beach here and there when filming in our Magic City, but when your announcers show shots of the arena saying ‘live from South Beach…,’ not only is it inaccurate but to be honest, it hurts our feelings,’’ read a light-hearted DDA email sent to the cable broadcaster during the 2011 championship season.

As Miami enjoys its third championship run during the James reign, downtown’s promoters have all but declared victory.

They see images of the city’s revived skyline and bustling restaurant district as having replaced South Beach’s surf and sand as the default backdrop for Heat games. And while Thursday’s downpours may have cut into video cuts to outside AmericanAirlines Arena for Game 1, downtown’s marketing arm sees the imaging shift as complete. Schwartz Media, the DDA’s publicity firm, no longer mentions South Beach in its pitches to broadcasters, but instead offers a menu of potential backdrops throughout the downtown area.

“You can’t buy better than images than what we have seen,’’ said DDA director Alyce Robertson. “We’ve come into our own. The image of Miami is not the palm trees on the beach.”

Her comments and the DDA’s retired positioning campaign touch on a sensitive topic in Miami-Dade County’s tourism circles, where vacation marketing can get complicated. Surveys show South Beach is the most popular tourism destination in the region, and the county’s tax-funded tourism bureau centers its advertising campaigns around “Miami” — no matter the city limits.

“The Miami brand is the entire community,’’ said William Talbert, president of the Greater Miami Convention and Visitors Bureau. “The visitor doesn’t know political jurisdictions. South Beach is Miami. Everybody knows South Beach.”

For downtown, the James arrival coincided with a wave of optimism downtown. As the recession ended, a surge of condo purchases and retail openings signaled a new vibrancy for Miami’s urban waterfront. The Heat’s sudden status as the hottest team in professional sports was touted as another sign of Miami’s revival after its empty and over-priced condo towers played a leading role in coverage of the national housing bust.

But with James calling South Beach his new home (despite buying a waterfront mansion in Miami’s Coconut Grove), downtown’s marketers saw a mixed message. “When he came out and said he was going to South Beach,” Robertson said, “I remember thinking: The arena where he plays is a downtown facility.”

She credits both the DDA’s publicity efforts and a more organic game of catch-up from the public as Miami gets attention for its restaurants, cultural offerings, real-estate scene and the construction of two new museums next to the Heat’s home at AmericanAirlines Arena. “South America has always loved urban Miami,’’ Robertson said. “Now I think that Americans are starting to appreciate it.”

Beach scenes still populate the “B-roll” that has accompanied Heat footage during the playoffs, and many broadcasters still use South Beach as a go-to substitute for a trip to the Miami area. “I have certainly not noticed a decline in the generalization of South Beach,’’ said Graham Winick, who heads up the Miami Beach office charged with coordinating film and television shoots in the resort city. “We think it’s fantastic.”

During this playoff season, the DDA backed off its defensive position and sees the NBA Finals as an easy source of valuable footage between commercial breaks. Banners throughout the city feature James and teammate Dwyane Wade posing with dancers from the Miami City Ballet, and the Downtown Development Authority heads a campaign to bathe as many buildings as possible in white light during games. The Intercontinental Miami hotel uses its new 19-story video display to scroll “Let’s Go Heat” on a white LED canvas during the playoffs, and shifts into a frenzied red wave after a win.

“The blimp has been focusing on it every game during the last couple of series,” said Robert Hill, general manager of the Intercontinental. “One night, somebody told me they saw it eight times.”

Tim Corrigan, supervising producer for ESPN’s upcoming coverage of the NBA finals, said camera crews have been in Miami Beach and downtown this week collecting scenic footage to sprinkle throughout the broadcasts on ABC. (Both companies are owned by Disney.) He said night games favor the skyline of Miami, but that he considers South Beach to be a natural part of the scenery, too.

“When I say the city, it’s downtown plus South Beach,’’ he said. “The quote is very famous. I don’t think we take it as literally as that. He took his talents to Miami. That’s ultimately what he did.”